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Logistic Carrying Capacity from Population Growth

Rearrange the continuous logistic growth equation to estimate carrying capacity from population, intrinsic growth rate and observed growth, with retained inverse calculations.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

With population 100, intrinsic rate 0.2 per year and instantaneous growth of 10 individuals per year, the logistic relation gives a carrying capacity of 200.

C = rN(1 − N/K); K = N / [1 − C/(rN)]

Worked example

Enter these known values and leave the other values blank.

Current modeled population N
100
Intrinsic rate r (decimal per same time)
.2
Instantaneous change C (individuals per time)
10
Logistic carrying capacity K
200

Assumptions and limitations

  • Use the same time unit for the intrinsic rate and population change. Enter 0.2 for 20% per time unit; this field is a decimal rate, not a percent selector.
  • N, K and r must be positive. For finite positive K, the population growth C must be below rN; equality corresponds to no finite carrying capacity.
  • Zero change with positive r and N gives K = N. Negative change is allowed and corresponds to a population above carrying capacity in this model.
  • Solving for N is generally not unique. The retained source inverse returns the larger quadratic root; a smaller positive root may also fit the same K, r and positive C.
  • Treat C as an instantaneous derivative. A finite-period population difference is only an approximation, and this algebraic result does not establish that a real population follows constant-parameter logistic growth.

Common questions

Why can the population inverse give two answers?

Logistic growth rises up to N = K/2 and then falls. The same positive growth below its maximum can occur below or above K/2; this calculator retains the larger root.

References

Bookify requires a positive intrinsic logistic rate and a finite positive carrying capacity while preserving zero and negative population growth.

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